Symmetric Matrix

A square matrix whose elements above the main diagonal are mirror images of the elements below the main diagonal is called a symmetric matrix. Alternatively, a symmetric matrix is such that its transpose is equal to itself; that is, A = A'. That is, the element aij of A is equal to the element aji of A'. An example is the variance-covariance matrix given in equation (C.2.2). Another example is the correlation matrix given in (C.5.1).


Null Matrix

Null Vector

Equal Matrices

A matrix whose elements are all zero is called a null matrix and is denoted by 0.

A row or column vector whose elements are all zero is called a null vector and is also denoted by 0.

Two matrices A and B are said to be equal if they are of the same order and their corresponding elements are equal; that is, aij = bij for all i and j. For example, the matrices

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